Codes and Expansions (CodEx) Seminar

Michael Catanzaro (Geometric Data Analytics, Inc.):
Topological Parallax: A Geometric Specification for Deep Perception Models

In typical deep learning applications, models like deep neural networks can be trained to 100% accuracy with exceptional performance on validation sets but poor generalization performance on unseen data. We characterize this misalignment between model and data as the failure of a geometric property which is essential to trustworthy interpolation and perturbation. We introduce topological parallax to quantify the topological mismatch between model and data and using the tools of algebraic topology, we show parallax is stable to interpolation and noise perturbation. Parallax can indicate whether the model shares similar stable multiscale geometric features with its training dataset and thus provide better generalization guarantees. We will assume little topological and deep learning backgrounds and will explore these ideas through a variety of examples.